intermediate algebra applications visualization 3rd edition rockswold solutions manual

IASM_IA_523555.qxp 3/18/08 3:43 PM Page iii TABLE OF CONTENTS Introduction iv General, First-time advice Sample Syllabi Teaching Tips Correlated to Textbook Sections 15 Extra Practice Exercises 47 Available Supplements 69 Useful Outside Resources for Teachers 75 IASM_IA_523555.qxp 3/18/08 3:43 PM Page iv INTRODUCTION Dear Faculty: The Rockswold/Krieger book team at Pearson Addison-Wesley is very excited that you will be using Intermediate Algebra with Applications and Visualization, Third Edition We know that whether you are teaching this course for the first time or the tenth time, you will face many challenges, including how to prepare for class, how to make the most effective use of your class time, how to present the material to your students in a manner that will make sense to them, how best to assess your students, and the list goes on This manual is designed to make your job easier Inside these pages are words of advice from experienced instructors, general and content-specific teaching tips, a list of the topics covered within the Intermediate Algebra with Applications and Visualization text, descriptions of both student and instructor supplements that accompany this text, and a list of valuable resources provided by your fellow instructors We would like to thank the following professors for sharing their advice and teaching tips This manual would not be what it is without their valuable contribution William P Fox, Francis Marion University Debbie Garrison, Valencia Community College Jolene Rhodes, Valencia Community College Dr C.B Gubitose, Southern Connecticut State University Marilyn Prine, Tomball College It is also important to know that you have a very valuable resource available to you in your Pearson AddisonWesley sales representative If you not know your representative, you can locate him/her by logging on www.aw-bc.com/replocator and typing in your zip code Please feel free to contact your representative if you have any questions relating to our text or if you need additional supplements We know that teaching this course can be challenging We hope that this and the other resources we have provided will help to minimize the amount of time it takes you to meet those challenges Good luck in your endeavors! The Rockswold/Krieger book team IASM_IA_523555.qxp 3/18/08 3:43 PM Page GENERAL, FIRST-TIME ADVICE We asked the contributing professors for words of advice to instructors who are teaching this course for the first time or for the first time in a long while Their responses can be found on the following pages Debbie Garrison, Valencia Community College This textbook stresses the rule of (algebraic solutions, numerical solutions, graphical solutions, and writing about problems) Make sure that you use all these techniques in your explanations and examples It is not necessary to every problem all different ways, but try to vary your approach so students see all methods every class or at least every week Do some problems using more than one approach Connections between algebraic, numerical and graphical solutions should be emphasized Show the students how the answer they get using algebra and the entries in the table are related Show them where the algebraic solution corresponds to the point(s) on a graph Model for your students the correct interpretation of all solutions Require them to answer problems with complete sentences Don’t be afraid to use examples with “messy numbers.” Use fractions, decimals, and negative numbers as coefficients If every example you in class turns out to have whole number answers, students will think they have done something wrong when their homework answers are not whole numbers Try to problems other than the text examples in class; that way, the students will have the examples in the textbook as another source of problems to model If students are using a graphing calculator in this class, model its use and show them the keystrokes as you go I always set up my overhead calculator prior to every class and use it as I suspect a student would to solve the problem I teach keystrokes the first time I use a key or operation and just call out the keystrokes as I use them from then on Discussions about order of operations and alternative methods of solution can be introduced once the basics are mastered I try to only show one or two new calculator operations per class This way the students are not overwhelmed by the technology and can concentrate on the problem solving This text emphasizes applications and modeling Do application problems in class and assign them for homework If you only and assign the skill and drill problems, you are defeating the purpose and strength of this text Try to model correct mathematical terminology and notation in class Students will mimic what you in solving problems If you are careless with notation, skip steps, neglect to define variables, or fail to interpret answers, so will they Have fun, use interesting examples, and show your enthusiasm for mathematics Enjoyment of the topic can be contagious William P Fox, Francis Marion University This advice is from both a department chair and an instructor of the course Make sure you know your department’s expectations for students completing this course Make sure you know whether graphing calculators are allowed in the follow-on courses before you make it available in your course Most students are placed in an intermediate algebra course because of their placement scores There had to have been some disconnection between the student’s high school algebra I and II and their ability to retain enough critical knowledge to move past a course such as this A college teacher should not just stand at the board and work examples from the book, assign homework from the book, and test that same material A college teacher motivates the learning of the material and facilitates students to comprehend and make solid connections with the material Use the rule of four (symbolic, graphical, numerical, and interpret the results) often Have the students work problems in class and maybe even have them work some at the boards If you work all General, First-Time Advice IASM_IA_523555.qxp 3/18/08 3:43 PM Page Instructor and Adjunct Support Manual Intermediate Algebra with Applications and Visualization, Third Edition the problems, the only thing you know for sure is that you can solve the problems We want the student to be able to solve the problems Personally, I not spend a lot of time on basic factoring skills These were learned in high school and forgotten The skill will not mysteriously reappear after our 1–3 lessons Rather, I cover the purpose of factors and the result of factoring, graphical techniques, and the quadratic formula (for all quadratic equations—because it always works in both real and complex situations) Basic factoring works for simple integers and gets more difficult for students as problems increase in difficulty Teach the quadratic formula and then “back” into the Fundamental Theorem of Algebra I have found this works I have come to realize that in mathematics our use of symbols and “names” often confuses students For example, consider the “Distance” formula Students might remember this as either D = RT or 2(x1 - x2)2 + (y1 - y2)2 Students coming from high school have been trained not to read the mathematics textbooks from grades K–12 We must break this habit Ensure that the students have pre-read the material and tried a few basic problems prior to your lecture Grade them daily on basic topics from the reading in an effort to break this trend Make your class interactive, if possible Use technology to allow students to discover concepts and connections rather than you just telling them a sequence of facts As a college mathematics teacher, you must know how this course integrates into the curriculum and whether it counts for General Education credits Teach the course from the aspect of the gaining instructor Emphasize the critical material over the mundane Do not teach this course as if everyone will become a mathematics major It is true that less than 1% of all college students move into mathematics Teach it from the standpoint of usefulness to the curriculum and the usefulness of mathematics in the 21st century Not everything written in a textbook is critical information that has to be taught Textbooks are written generally enough to allow flexibility Use this flexibility Include modeling applications (or real world applications) to motivate the material This answers the question, “Why am I learning this?” before it is asked I start every chapter and many sections with a motivating problem and then spend the time covering the material that allows for the solution Allow students time to experiment, conjecture, and discover Too often we like to “show and tell” and we would be more robust educators if we allow students time to discover some things on their own Jolene Rhodes, Valencia Community College Make your expectations clear to the students For example, if application problems are important, then they need to be discussed in class and assigned for homework as often as possible If this is the first course where students are required to use a graphing calculator, be sure to take one to class and explain the keystrokes needed for new types of calculations It is not easy to learn by reading the instruction manual that comes with the calculator Sometimes a class of students will not keep to a schedule that you designed before the course starts They may need an extra day for some topics and less time for others Be a little flexible but don’t get so far behind that you cannot finish the material It is important to stress solving graphically, numerically, and symbolically throughout the course Students should understand the connections and be capable of using one method of solution to check answers they found using a different method Some students will prefer using one method and you need to decide if you want them to choose a method or you want to specify which method they should use when you are testing the material Marilyn Prine, Tomball College When considering pacing for the course, expect to spend extra time on Chapter Students find this chapter the most difficult As you move through the chapters, try to make as many connections to past and future chapters as possible For example: Extraneous solutions in Chapter and Inverse vocabulary in Chapter 1, 6, and “Isolate the absolute value” in 3.5 and “Isolate the radical” in 7.5 Reading function values from graphs in Sec 2.1, 2.2, 5.1, 6.1, 8.1 Make sure students are successful factoring in Chapter since factoring is used heavily in Chapter and some in Chapter IASM_IA_523555.qxp 3/18/08 3:43 PM Page SAMPLE SYLLABI Provided by: Francis Marion University Valencia Community College Sample Syllabi IASM_IA_523555.qxp 3/18/08 3:43 PM Page Instructor and Adjunct Support Manual Intermediate Algebra with Applications and Visualization, Third Edition MATH 105, COLLEGE ALGEBRA I WITH ANALYTIC GEOMETRY SYLLABUS Instructor: Office: Phone: Office Hours: Dr William Fox Text: Intermediate Algebra with Applications and Visualization, Rockswold/Krieger, AW Additional Resources: The instructor is available during office hours and at other times (by appointment) to provide extra assistance with the course material Please take advantage of this resource MW 1:30–3:00 TTh 9:00–11:30, 2:10–3:00 Other times by appointment Computer tutorials and instructional videos are available as a supplement to the text These would be excellent extra resources to assist in mastering the materials presented in class and in the text book See the instructor for information on how to access these materials Tutors in all subject areas are available in the afternoons in the University Center These tutors are available to you free of charge For a list of paid, private tutors, see your instructor or the math secretary Calculator Objectives: Graphing calculator will be allowed after Test The goals of this course are to have the student Be able to compute with integers additional numbers, locate such numbers on the real number line, identify numbers as whole, integer, rational or irrational, and answer relative conceptual questions Learn to compute using the order of operations, evaluate certain roots, simplify exponential expressions, use the field properties, and answer conceptual questions Be able to combine like terms, solve linear equations and inequalities in one variable (graphing the solution sets of the latter), and demonstrate skill in modeling mathematically Be able to solve and graph solution sets of compound linear equations and inequalities in one variable, solve linear inequalities involving absolute value, and model inequalities Be able to graph lines and linear inequalities in two variables, derive the equations of lines given certain characteristics, identify functions and relations and their domains, and solve variation problems Be able to solve systems of linear equations in two variables graphically and algebraically, be able to solve systems of linear equations in three variables, and be able to model in two variables Requirements: Regular attendance is required The instructor reserves the right to withdraw any student who is absent from more that class meetings It is the student’s responsibility to get a copy of the class notes and the homework assignment for any days missed Students are responsible for completing assigned problems as we complete each section Assignments are given by section in Appendix A of the syllabus Additionally, students are responsible for reading ahead to the next section of the text Approximately once a week there will be a 10–15 minute announced quiz on the IASM_IA_523555.qxp 3/18/08 3:43 PM Page Sample Syllabi homework materials or a separate homework assignment to be submitted for a grade Homework/Quiz grades will account for 15% of the final grade Students will not be allowed to make up missed quizzes or homework, but a couple of the grades will be dropped at the end of the semester There will be chapter tests given, the tentative dates of which are given in the attached schedule (any change to these dates will be announced at least a week in advance of the new date) Students should be present for all tests Make-ups for missed tests will be permitted only in the case of verifiable medical emergency If you know in advance, however, that you have a conflict with a test date, you should discuss with your instructor the possibility of taking the test early Each test will account for 15% of the final grade There will be a comprehensive final exam given at the date and time listed on the attached schedule All students must be present for the exam to receive credit for the course If a student has more than exams scheduled for one day, the student may request permission from the instructor to take the exam at an alternate date/time Such arrangements must be made by Reading Day Any other absences from the final exam will result in a grade of F for the course unless approved in writing by the Provost The final exam will account for 25% of the final grade Summary of Grading Procedure: Composition of Final Grade: Weekly grades 15% Test 15% Test 15% Test 15% Test 15% Final Exam 25% Grading Scale: 90–100 85–89 80–84 75–79 70–74 65–69 60–64 Below 60 A B+ B C+ C D+ D F Please note that you must earn a grade of C or better to proceed to Math 111 Important Dates: September (Labor Day) September 25 October 14 November & November 20 November 26 & 27 December December December Classes will meet Last day to withdraw without penalty* Midterm Fall Break (no classes) Last day to withdraw with possible penalty Thanksgiving Break (break begins at 12:30 pm on Wednesday, November 25) Last day of classes Reading Day Exams begin *Please be aware that withdrawals after September 25 will be issued with a grade of either passing or failing depending upon your average at that time If you receive a W/F (withdraw/failing) grade, it does affect your GPA Withdrawals on or before September 25 will be issued a grade of W, which does not affect your GPA You should also consider the number of credit hours you are carrying before making the decision to withdraw If you drop below 12 credit hours, you may no longer be considered a full-time student This may affect your financial aid and your health insurance if you are insured by your parents IASM_IA_523555.qxp 3/18/08 3:43 PM Page Instructor and Adjunct Support Manual Intermediate Algebra with Applications and Visualization, Third Edition Tentative Schedule: 8/28 8/31 9/2 9/4 9/7 9/9 9/11 9/14 9/16 9/18 9/21 9/23 9/25 9/28 9/30 10/2 10/5 10/7 10/9 10/12 10/14 10/16 10/19 10/21 10/23 10/26 10/28 10/30 11/2 11/4 11/6 11/9 11/11 11/13 11/16 11/18 11/20 11/23 11/25 11/30 12/2 12/4 12/7 Intro and Section 1.1 1.1 1.2 1.3 1.4 1.4 1.5 Review for Test Test NO CALCULATORS 2.1 2.1 and 2.2 2.2 2.3 2.3 2.4 2.4 Review for Test Test 3.1 3.1 3.2 3.2 3.3 3.3 3.4 3.4 Review for Test Test Fall Break – No Class 4.1 4.1 4.2 4.2 4.2 4.3 4.4 4.4 4.5 4.5 Review for Test Test NO CALCULATORS Project: Chemical Balancing Review for Final Exam IASM_IA_523555.qxp 3/18/08 3:43 PM Page Sample Syllabi MATH 111 – INTERMEDIATE ALGEBRA Dr William P Fox, Chairman and Professor Office # Office Phone # Office Hours: TBD E-mail Text: Intermediate Algebra with Applications and Visualization, Rockswold/Krieger, AW Goals: Students should be able to use algebra properties to solve real world problems Students will learn to work in groups as well as use technology to assist in the solving of problems Students will learn how to model and think critically with algebraic equations Topics: Review of Linear Functions and solving of Linear Equations Polynomials: form, properties, factoring Rational Expressions: properties, uses, and equations Roots and Radicals: properties, uses, and equations Quadratic Equations: 2nd order polynomials, quadratic formula 2b2 - 4ac 2a Graphs and formulas of Nonlinear Functions: Parabolas, Circles, Hyperbolas, and Ellipses Exponential and Logarithmic Functions Mathematical Models -b; Grading: Portfolio Quizzes: 4@50 Points Projects: 3@200 Major exams: 5@120 Comprehensive Final Total 100 Points 200 Points 600 600 200 points (all students must take) 1700 points Class Time: 08:30–09:20 MWF Student Requirement: A specific graphing calculator is required and will help you throughout this course Attendance Policy: Any students who miss more than classes will be dropped from the course Portfolio: This is a notebook that contains all critical definitions, old projects, quizzes, student essay and reflections, and study notes Grades: 90–100 85–89.99 80–84.99 75–79.99 70–74.99 65–69.99 60–64.99 5 AND x5 OR x